Vein like structures on surface of testicle

I have always had an irrational phobia of touching my testicles from an early age in case I happen to find something "nasty". Around a year or so ago I noticed what feels like a vein or thin tube running from about half way down each testicle to the epididymis at the bottom. These feel preety mush the same on each testicle and after leaving the testicle itself, seem to form part of the epididymis.

Recently, I noticed a second similar structure on my left testicle. This runs along the surface for around 1 CM then leaves and travels up into my abdomen with the other cords. I think I may also have a third, similar structure on my left testicle but cannot be sure.

Logically, I know that this cannot be a tumour or something as it is not growing from inside the testicle, does not feel like a pea sized lump and connects to other parts of my anatomy (the epididymis in one case and my abdomen in the other). I still worry though as I cannot find any reference online to these types of structure.

Can anyone explain what it is that I can feel. Just to clarify, the tubes above my left testicle are thicker than the right so think this may be a varicocele.